PROJECT SUMMARY/ABSTRACT Statistical Models for Group Comparison of Functional MRI Data Recently, many large-scale neuroimaging datasets have been collected and analyzed in an attempt to elucidate brain activities including but not limited to the pathology of psychiatric disorders and cognitive brain functions. However, only a few approaches have been developed for simultaneously analyzing multi-subject neuroimaging data. In this project, we will propose statistical models for integrating functional connectivity pattern across subjects. We will consider two types of data collected in different ways: 1) multi-subject functional MRI data obtained from one or more populations, and 2) multi-subject repeated-measures fMRI data obtained from one or more populations. For the first type of data, we will develop a dimension reduction method which considers spatial and temporal dependency. The spatial maps extracted will be used to detect group differences and further for image classification. While taking spatial and temporal correlations into account, we will study statistical procedures involved in the sparse estimation algorithm, including the choices of the weight function, bandwidth, and tuning parameter. In addition, we will examine how to measure spatial and temporal similarity between two brain voxels in order to impose a weight on the neighboring voxels. Furthermore, we will study the functional connectivity patterns for different groups by estimating penalized correlation functions. The proposed connectivity method will be verified by using simulation studies and acquired fMRI datasets. For the second type of data, we will consider three special cases: 1) repeated- measures fMRI data that do not depend on age or time, 2) longitudinal fMRI data, and 3) longitudinal fMRI data with different spatial resolutions. In a further aim, we will develop statistical models to address these special cases which can be generalized into a unified model framework. Then, we will establish testing procedures to detect group differences for each case. In summary, we will study statistical models to analyze multi-subject fMRI data collected in various ways, and also consider spatial-temporal correlations as well as high- dimensionality of the data for proposing new statistical procedures such as model selection criteria. The proposed research is important because it addresses the essential steps for analyzing highly correlated fMRI data for multi-subject and multi-group conditions. By applying the proposed models, we will be able to detect group differences with increased power. Moreover, the statistical models we will develop will help us to address research questions effectively in multi-subject fMRI studies.